Dynamics of test particles, QPOs and thermodynamics of charged Euler-Heisenberg AdS black holes with a cloud of strings and dark matter

Abstract We investigate the geodesic motion of test particles around a charged Euler-Heisenberg Anti-de Sitter black hole (CEH-AdS-BH) with a cloud of strings (CoS) and surrounded by perfect fluid dark matter (PFDM). Our analysis examines how the interplay between Euler-Heisenberg nonlinear electrodynamic corrections, string cloud, and PFDM distributions modifies fundamental BH properties. We study dynamics of both massless photons and massive neutral test particles, deriving the effective potentials and trajectory equations that govern particle motion in this exotic spacetime. The photon sphere analysis shows systematic increases in shadow radii with string cloud parameter variations, while innermost stable circular orbit (ISCO) calculations demonstrate competing effects between string-induced gravitational weakening and electromagnetic charge contributions. We examine scalar and electromagnetic field perturbations using the Klein-Gordon and Maxwell equations, establishing the perturbative potentials that characterize wave propagation in the modified background. The scalar perturbative potential exhibits characteristic barrier structures influenced by all exotic matter components, while electromagnetic perturbations show fundamental differences due to their vector nature. We compute the quasinormal mode (QNM) spectrum using the WKB approximation and compare predicted epicyclic frequency ratios with observed quasi-periodic oscillation (QPO) data from the microquasar GRO J1655-40. Our thermodynamic investigation extends the conventional framework by incorporating additional intensive variables corresponding to cosmic string and perfect fluid dark matter contributions. We derive the generalized Smarr relation, identifying anomalous contributions from the PFDM logarithm and Euler-Heisenberg nonlinearity. The specific heat capacity analysis reveals divergence points that demarcate thermodynamically stable and unstable regions, while the Gibbs free energy exhibits modified profiles that extend Anti-de Sitter black hole thermodynamics into new parameter regimes.